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On the integro‐differential equations with reflection
Author(s) -
Ait Dads Elhadi,
Khelifi Safoua,
Miraoui Mohsen
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6693
Subject(s) - mathematics , lipschitz continuity , uniqueness , exponential dichotomy , mathematical analysis , reflection (computer programming) , measure (data warehouse) , differential equation , exponential function , nonlinear system , variable (mathematics) , pure mathematics , programming language , physics , quantum mechanics , database , computer science
In this paper, by developing important properties on the composition of functions with reflection, using some exponential dichotomy properties and an application of the fixed‐point theorem, several new sufficient conditions for the existence and the uniqueness of an pseudo almost automorphic solutions with measure for some general‐type reflection integro‐differential equations. We suppose that the nonlinear part is measure pseudo almost automorphic and in which we distinguish the two constant and variable cases for the Lipschitz coefficients of the functions associated with this part. It is assumed that the linear part of the equation considered admits an exponential dichotomy. Finally, an application is given on the very interesting model of Markus and Yamabe.